Hydrodynamic forces in the drainage of an electrolyte confined between dielectric surfaces

We present a theory for the hydrodynamic forces in the drainage of an electrolyte film confined between charged curved surfaces, which applies to small gaps under local equilibrium across the film thickness. We derive a local Onsager formalism describing the coupled flow rate, charge and solute fluxes, which accounts for all degrees of overlap of the electrical double layers (EDLs) and can be adapted to a variety of electrical, chemical or hydrodynamic boundary conditions. We explore in detail the case of a monovalent electrolyte with constant surface charge and no-slip boundary conditions. A complete phase diagram is established for the electro–kinetic damping, including non-overlapping EDLs at both high and low Dukhin numbers, as well as all degrees of EDLs overlap including the Gouy–Chapman, Debye–Hückel and ideal-gas domains. We highlight a simple relation between the apparent hydrodynamic distance at high Dukhin number and the surface electrical conductance. Our theory also predicts a diffusio–kinetic contribution to the so-called electroviscous effect, which does not reduce to a damping but exhibits a conservative (stiffness) component. We show that this stiffness decays as an algebraic function of the gap between the surfaces and may dominate the stiffness due to the equilibrium Derjaguin–Landau–Verwey–Overbeek interaction force.